Multi-Step Word Problems

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ISEE Middle Level: Quantitative Reasoning › Multi-Step Word Problems

Questions 1 - 10
1

A farmer is building a straight fence that is 120 meters long. He places a fence post at the start of the fence and then a post every 3 meters. If each fence post costs $7, what is the total cost of all the fence posts needed?

$280

$287

$294

$840

Explanation

First, determine the number of 3-meter sections in the fence: \(120 \text{ meters} \div 3 \text{ meters/section} = 40\) sections. For a straight fence with posts at both ends, the number of posts is one more than the number of sections. So, the farmer needs \(40 + 1 = 41\) posts. Finally, calculate the total cost of the posts: \(41 \text{ posts} \times \$7/\text{post} = \$287\).

2

A school is planning a field trip for 130 students and 12 adults. Each bus can hold a maximum of 48 people. What is the total number of empty seats on all the buses used for the trip?

2

14

46

50

Explanation

First, find the total number of people going on the trip: \(130 + 12 = 142\) people. Next, determine the minimum number of buses needed by dividing the total people by the bus capacity: \(142 \div 48 = 2\) with a remainder of 46. Since there is a remainder, 3 buses are needed. Then, calculate the total number of seats on 3 buses: \(3 \times 48 = 144\) seats. Finally, subtract the number of people from the total number of seats to find the number of empty seats: \(144 - 142 = 2\).

3

To earn an A in science, Jordan needs an average of at least 92 on five tests. His scores on the first four tests are 88, 95, 86, and 94. What is the minimum score Jordan must get on the fifth test to earn an A?

92

95

97

98

Explanation

First, find the total score Jordan needs across all five tests to have an average of 92. This is \(5 \times 92 = 460\). Next, find the sum of his scores on the first four tests: \(88 + 95 + 86 + 94 = 363\). Finally, subtract the sum of the first four scores from the target total score to find the required score on the fifth test: \(460 - 363 = 97\).

4

A charity fundraiser receives donations from 120 people. The average donation is $25. A local company agrees to match every dollar donated above a total of $2,000. How much money will the company donate?

$1,000

$2,000

$5,000

$3,000

Explanation

First, calculate the total amount of money donated by the people: \(120 \text{ people} \times \$25/\text{person} = \$3,000\). The company matches the amount donated above $2,000. To find this amount, subtract the threshold from the total donations: \(\$3,000 - $2,000 = $1,000\). The company will donate this matched amount, which is $1,000.

5

A recipe for 6 servings uses 1.50 cups rice and 3.00 cups broth; what are the adjusted ingredient amounts for 15 servings?

Use 1.50 cups rice and 3.00 cups broth

Use 3.75 cups rice and 7.50 cups broth

Use 4.50 cups rice and 9.00 cups broth

Use 2.50 cups rice and 5.00 cups broth

Explanation

This question tests ISEE Middle Level quantitative reasoning skills, specifically solving multi-step word problems using the four operations. Multi-step problems require students to apply the correct sequence of operations to reach a logical solution, often requiring addition, subtraction, multiplication, and division. In this problem, students must scale a recipe from 6 to 15 servings, executing calculations in the correct order. The correct answer is achieved by finding the scaling factor (15 ÷ 6 = 2.5), then multiplying each ingredient: rice (1.50 × 2.5 = 3.75 cups) and broth (3.00 × 2.5 = 7.50 cups). A common distractor might involve using an incorrect scaling factor or only scaling one ingredient. To help students: Teach them to always find the ratio of new servings to original servings first, then apply this factor consistently to all ingredients.

6

A bag of 96 candies is to be shared among three friends: Amy, Beth, and Carla. Amy gets \(\frac{1}{4}\) of the candies. Beth gets \(\frac{1}{3}\) of the remaining candies. Carla gets the rest. How many more candies does Carla get than Amy?

16

24

32

48

Explanation

First, find how many candies Amy gets: \(96 \times \frac{1}{4} = 24\) candies. Next, find the number of remaining candies: \(96 - 24 = 72\) candies. Then, find how many candies Beth gets from the remainder: \(72 \times \frac{1}{3} = 24\) candies. Carla gets the rest, which is \(72 - 24 = 48\) candies. Finally, find the difference between Carla's and Amy's shares: \(48 - 24 = 24\) candies.

7

An employee earns $15 per hour for the first 40 hours worked in a week. For any hours worked over 40, the employee earns 1.5 times the regular hourly rate. If the employee worked 46 hours in one week, what were their total earnings for that week?

$690.00

$1,035.00

$699.00

$735.00

Explanation

First, calculate the earnings for the first 40 hours: \(40 \text{ hours} \times \$15/\text{hour} = \$600\). Next, determine the number of overtime hours: \(46 - 40 = 6\) hours. Then, calculate the overtime rate: \($15 \times 1.5 = $22.50\) per hour. Calculate the overtime earnings: \(6 \text{ hours} \times \$22.50/\text{hour} = \$135\). Finally, add the regular earnings and overtime earnings: \($600 + $135 = \$735.00\).

8

A recipe for a batch of cookies requires \(\frac{3}{4}\) cup of sugar. Liam wants to make 3 batches of cookies. He starts with a bag containing 4 cups of sugar. After making the cookies, how much sugar is left in the bag?

\(1 \frac{1}{4}\) cups

\(2 \frac{1}{4}\) cups

\(1 \frac{3}{4}\) cups

\(3 \frac{1}{4}\) cups

Explanation

First, calculate the total amount of sugar needed for 3 batches. This is \(3 \times \frac{3}{4} = \frac{9}{4}\) cups. Convert the improper fraction to a mixed number: \(\frac{9}{4} = 2 \frac{1}{4}\) cups. Then, subtract the amount of sugar used from the initial amount: \(4 - 2 \frac{1}{4} = 1 \frac{3}{4}\) cups.

9

A school bake sale sells brownies for $1.50 each and cookies for $0.75 each. The ingredients cost a total of $45. If they sell 60 brownies and 80 cookies, what is the total profit from the bake sale?

$90

$105

$150

$195

Explanation

First, calculate the total revenue from selling brownies: \(60 \times $1.50 = $90\). Next, calculate the total revenue from selling cookies: \(80 \times $0.75 = $60\). Then, find the total revenue: \($90 + $60 = \$150\). Finally, calculate the profit by subtracting the cost of ingredients from the total revenue: \(Profit = Revenue - Cost = \$150 - $45 = $105\).

10

Maya withdrew some money from her bank account. She spent $35 on a shirt. Then she gave half of the remaining money to her brother. If she has $40 left, how much money did she withdraw from her account originally?

$75

$90

$115

$150

Explanation

This problem is best solved by working backward. Maya has $40 left after giving half of her money to her brother. So, before giving him money, she had \(\$40 \times 2 = \$80\). Before that, she spent $35 on a shirt. To find the amount she had before the purchase, add that amount back: \($80 + $35 = \$115\). This was the amount she originally withdrew.

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